Not really
A closer comparison would be between life in Eden and life as depicted in Isaiah 65.
The notion of the Kingdom of God has a fairly precise content - immortality in God’s favour does not by itself have much to do with the KoG. The idea of the KoG has a long history in both Testaments; it expresses how God reigns over men, among men, and - at least for Israel - seems to presuppose ideas of creation and election. After all, God had to create & choose Israel, in order to be Israel’s King. The notion of creation goes with the paradisal conditions of Isa. 65 & Genesis 1-3; but kingship less so.
That God does reign over & among His people, was the stable core of the idea - others, such as the covenant with David and his heirs, and Messianism, grew out of it: until in the Gospel we have Jesus preaching the Kingship of God: but not a crassly political kingdom; instead, the Kingdom He preaches is established in the hearts of men, rather than being the kind of Kingdom in which Israel would be Top Nation: which was an older form of the idea. ##